I was always under the impression that for an object to be a planet it had to have a satellite orbiting around it, a moon, that is why Pluto can be called a planet even though it is so small. My question then is, why are Mercury and Venus planets and what are the parameters required for planet status.

Since the original submission of this question (in 1999), Pluto has been demoted to a dwarf planet, instead of just a planet.

Not all planets have moons (you've pointed out that Venus and Mercury do not), and that's not a requirement.

In 2006, the International Astronomical Union (IAU), which has the final say on matters of astronomical nomenclature, voted on a formal definition of what makes a planet. (The official press release is here.) According to their decision a planet must satisfy the following three criteria:

It must be an object which independently orbits the Sun (this means moons can't be considered planets, since they orbit planets)

It must have enough mass that its own gravity pulls it into a roughly spheroidal shape

It must be large enough to "dominate" its orbit (i.e. its mass must be much larger than anything else which crosses its orbit)

Because Pluto is not large enough to "dominate" its orbit, it is not a planet. (Neptune is about 8000 times more massive than Pluto, so Neptune is a planet and Pluto is a dwarf planet.)

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